In this paper we establish the space-like strong unique continuation for nonlocal equations of type (∂t−Δ)su=Vu, 0<s<1. The proof our main result, Theorem 1.1, is achieved via a conditional elliptic doubling property solutions to appropriate extension problem, followed by blowup analysis.

Abstract The space-time (ST) wave packet, a type of light source with many anomalous behaviors, has already found application in weak-field optics, however its generation method limits energy and therefore strong-field optics. Here we show that the type-I collinear optical parametric amplification (OPA) is natural amplifier for ST because it, spectrum (i.e., angle-dependent phase-matching spect...